Rewrite as a simplified fraction. ${1.\overline{13} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 113.1313...\\ 1x &= 1.1313...\end{align*}}$ Subtracting the two equations, we have: ${99x = 112}$ ${x = \dfrac{112}{99}} \text{or} {1 \dfrac{13}{99}}$